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lfunc_lfunctions • Show schema
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{'Lhash': '2176129479541550133331120494635', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0.7463654331365817, 0.7463654331365817], 'a4': [0, 0], 'a5': [0.8222318794986627, -0.8222318794986627], 'a6': [0, 0], 'a7': [6.8809060675854585, -1.2857416883128676], 'a8': [0, 0], 'a9': [0, -7.885877280437685], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.207115843341303, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-6.8809060675854585, 1.2857416883128676]]]], 'bad_primes': [2, 7], 'central_character': '448.433', 'coefficient_field': 'CDF', 'conductor': 448, 'conductor_radical': 14, 'conjugate': '994861569106912448473901307206', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.7463654331365817, -0.7463654331365817], [0, 9.0]], [[1.0, 0], [-0.8222318794986627, 0.8222318794986627], [0, -25.0]], [[1.0, 0], [-6.8809060675854585, 1.2857416883128676]], [[1.0, 0], [2.574227494024269, 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{'__RealLiteral__': 0, 'data': '0.1740176057189635', 'prec': 60}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.71666347110927652836562161401', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.61174811043727816508699360277', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.46305388221486040142095791999', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.207115843341303, 'bad_primes': [2, 7], 'central_character': '112.69', 'conductor': 448, 'conductor_radical': 14, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/448/3/l/b/433/15'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-448-112.69-c2-0-20', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-448-112.69-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.49386832083599, 'root_angle': 0.1740176057189635, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.71666347110927652836562161401', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2176129479541550133331120494635', 'Lhash_array': ['2176129479541550133331120494635'], 'label': '2-448-112.69-c2-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/448/3/l/b/433/15'}